Freestyle render - Problems getting it right
I'm very curious to see a better solution since I'm not very experienced with Blender myself, but perhaps this would work for you:


create a plane an add an Array modifier, with Constant Offset in the Z axis. The more duplicates you create the more lines you'll have in your final render.
select the object to be rendered and add a Boolean modifier.


Operation: Intersect
Object: plane

hide the array for rendering


Repeat with any other objects to create the horizontal lines.